A staggered‐grid multilevel incomplete LU for steady incompressible flows

Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this article, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

A Staggered Grid Multi-Level ILU for steady incompressible flows

We present a parallel fully coupled multi-level incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed in [1]. In this paper, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the wellknown 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

An Optimal Domain Decomposition Method for the C-Grid Navier-Stokes Jacobian

The Arakawa C-grid scheme is perhaps the most well-known discretization of the incompressible Navier-Stokes equations. The different variables (velocity components and pressure) are placed on the faces and in the center of the grid cells, respectively, to achieve good conservation and stability properties. In [De Niet and Wubs, IMA J. Num Anal. 2009] an optimal ordering of the variables for the sequential LU-decomposition of the resulting Jacobian was developed based on observations how fill is generated for such matrices during Gaussian elimination. In [Wubs and Thies, S!MAX 2011] the method was used in a domain decomposition approach and extended by a robust dropping strategy that leads to a preconditioner achieving a grid-independent convergence rate of GMRES. Structure-preserving properties of this incomplete LU (ILU) factorization allow recursive application and achieving optimal complexity of O(N log N) for scalar problems already. In this talk we show that this goal can be achieved for the 3D C-grid Navier-Stokes equations as well by using a special choice of space-filling subdomain shapes (parallelepipeda). We demonstrate results with this novel partitioning approach for both direct factorization and the multi-level ILU method on several thousand CPU cores. Possible applications include fully implicit time integration and bifurcation analysis of fluid dynamics problems

A Staggered Grid Multi-Level ILU for steady incompressible flows

We present a parallel fully coupled multi-level incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed in [1]. In this paper, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the wellknown 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

A staggered‐grid multilevel incomplete LU for steady incompressible flows

Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this article, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

Numerical modeling and quantification of droplet mixing using mechanowetting

Capillary forces are often found in nature to drive fluid flow, and methods have been developed aimed to exploiting these forces in microfluidic systems to move droplets or mix droplet contents. Mixing of small fluid volumes, however, is challenging due to the laminar nature of the flow. Here, we show that mechanowetting, i.e., the capillary interaction between droplets and deforming surfaces, can effectively mix droplet contents. By concentrically actuating the droplet, vortex-like flow patterns are generated that promote effective mixing. To quantify the degree of mixing, we introduce two strategies that are able to determine mixer performance independent of the initial solute distribution within a droplet, represented by single scalars derived from a matrix-based method. We compare these strategies to existing measures and demonstrate the full decoupling from the initial condition. Our results can be used to design efficient mixers, featuring mechanowetting as a new enabling technology for future droplet mixers